CN107292942A - A kind of weights C2Continuous linear hybrid shape editing method - Google Patents
A kind of weights C2Continuous linear hybrid shape editing method Download PDFInfo
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T13/00—Animation
- G06T13/20—3D [Three Dimensional] animation
Abstract
The invention discloses a kind of weights C2Continuous linear hybrid shape editing method, comprises the following steps：1) Back ground Information is obtained, includes model, real control point and the control bone of user's input；2) using real control point discretization control bone, and real control point is initialized；3) inner distance of each summit of appraising model to real control point；4) empty control point is generated；5) weight and the weight of dominating pair of vertices model vertices at the empty control point of real dominating pair of vertices are calculated；6) the real control point transformation of user's operation, empty control point response transform；7) GPU accelerates reconstruction model parallel.The present invention can be during editor, the original minutia of model surface is kept as far as possible, model deformation transitions smooth, it is capable of the partly or wholly shape of sensor model, the edit effect of model is good, the reconstruction model stage is accelerated using GPU parallel computations, and editor that can be in time to user feeds back, and efficient editorial efficiency can reach live effect.
Description
Technical field
The present invention relates to mould shapes editing technique field, a kind of weights C is referred in particular to2Continuously linear mixes Shape Editing
Method.
Background technology
Mould shapes editor and computer animation are closely bound up.Using editor algorithm or software editing into model, can
Using the key frame as animation, and by interpolation algorithm etc., animation sequence is generated.Computer animation can also by programming or
The methods such as animation soft, a series of scene model or the picture of scene are produced using computer graphic image Processing Algorithm
Face.Usually, present frame is the local modification of previous frame.Computer animation is reached by quickly continuously playing static picture
To the effect of visually object of which movement.In general, refresh rate is that more than 25 frame per second can allow human eye sensation it is seen that continuous
Visual effect.
2 D animation is to be used in the fields such as printing, drawing, advertisement at first, generation have gif file, MP4 files,
Flash and PowerPoint animations etc..2 D animation image is general represented by the bitmap or bivector figure of two dimension or
Editor.Include traditional animation techniques, Interpolation Deformation technology, Onion skinning algorithms and the contraposition interpolation of automation among this.
Three-dimensional animation be by animation teacher to model be digitized modeling and operation obtain.Animation teacher is general by creating
One 3D polygonal mesh, the operations such as a series of stretching, rotation are then carried out to it, the posture or scene of needs is deformed into
Deng.On grid, a series of point, side and the set in face are defined as in computer graphics, passes through the topology set
Relation is allowed to show fixed posture, and people can be allowed visually to form the scene of a three-dimensional model or three-dimensional.Have
When, grid model can provide internal digital skeleton structure and corresponding artis, allow users to facilitate operation model.
During motion or operation, software or algorithm can produce a series of key frame, then, then (be inserted by algorithm as linear
Value) enter row interpolation to the frame between key frame, generate corresponding animation sequence.
Closely during the last ten years, with the extensive use of three-dimensional grid model, many Shape Editing algorithms are in related field
It is suggested in succession.Existing model editing algorithm, be summarized as based on surface differential coordinate, based on barycentric coodinates and control grid,
Three class editor's algorithms based on covering interpolation.But by contrasting the above-mentioned first kind algorithm of discovery, some needs solution one
The system of linear equations of group belt restraining, the often solution of this algorithm eventually develops into one group of energy equation of minimum.It is this kind of to calculate
The calculating that method largely takes can influence the response speed that model is operated to user in editing process, while the principle of this algorithm
Do not allow readily understood.Above-mentioned Equations of The Second Kind algorithm is by constructing the mode such as bounding box or control grid, and then user passes through operation
Bounding box and control grid, affect indirectly model, reach the purpose of editor.The editor of this kind of algorithm is not directly perceived enough, Yong Huyao
Skill and experience, it is necessary to certain are operated to corresponding control unit.Moreover, this kind of algorithm some bounding box and control
Grid is Semi-Automatic Generation, and some algorithms need other software to generate bounding box and control grid, or even need user to participate in
The work of generation, it is impossible to adaptive all threedimensional models." candy paper effect " occurs in above-mentioned 3rd class algorithm, for there is one
The edit effect of fine deformation can not be reached to the editor for having the model of tiny characteristics by dividing, then, it is necessary to extra to this class model
Addition constraint.So existing algorithm can not meet simultaneously above-mentioned editor some require, lack a principle be readily appreciated that,
Efficiently, the editor's algorithm for being easy to operation to edit and work well.One editor's algorithm is mainly reflected in the edit effect of model
In deformation quality, the efficiency of editor and the easy operation of model, but existing most of algorithms are less able to above-mentioned three
Individual aspect all reaches preferable effect.Therefore, studying high-quality, the efficient edit methods for three-dimensional grid model is
Extremely it is necessary.
The content of the invention
It is an object of the invention to the shortcoming and deficiency for overcoming prior art, there is provided a kind of weights C2It is continuous linear mixed
Shape editing method is closed, this method can keep the original minutia of model surface as far as possible during editor, and model becomes
Shape transitions smooth, is capable of the partly or wholly shape of sensor model, and the edit effect of model is good, and the reconstruction model stage uses
GPU parallel computations accelerate, and editor that can be in time to user feeds back, and efficient editorial efficiency can reach live effect.
To achieve the above object, technical scheme provided by the present invention is：A kind of weights C2Continuous linear hybrid shape
Edit methods, comprise the following steps：
1) Back ground Information is obtained, includes model, real control point and the control bone of user's input；
2) using real control point discretization control bone, and real control point is initialized；
3) inner distance of each summit of appraising model to real control point；
4) empty control point is generated；
5) weight and the weight of dominating pair of vertices model vertices at the empty control point of real dominating pair of vertices are calculated；
6) the real control point transformation of user's operation, empty control point response transform；
7) GPU accelerates reconstruction model parallel.
In step 1) in, the model is the model to be edited of user's input, including the vertex set of model, model
Gather in face；The real control point and control bone refer to the real control dot position information of acquisition user's input and control bone two ends
Positional information.
In step 2) in, simulation control bone is removed with real control point, and real control point is initialized, comprise the following steps：
2.1) for the two ends of each control bone, simulation control bone is removed using two real control points respectively；
And then the real control point of initialization 2.2)：For for simulate control bone real control point, its frame N (nx,ny,
nz) first direction nxAlong the weighting direction of one or more control bones of connection, two other direction of frame is only
Need to meet with the orthogonal requirement two-by-two of first direction；For other real control points, frame N (nx,ny,nz)
Three directions be initialized as n respectivelyx=(1,0,0), ny=(0,1,0), nz=(0,0,1)；
In step 3) in, first to model voxelization, the fine and close voxelization result of model is obtained, then passes through the knot of voxelization
Fruit goes to appraising model summit to the inner distance at each real control point using the method for BFS.
In step 4) in, the real control point of user's input is possible to excessively sparse or excessively dense, for real control point
When being unsatisfactory for constraint, the empty control point of two classes of insertion comprises the following steps：
4.1) real control point and empty control point are referred to as control point, and Voronoi partitioning models are used centered on control point
Region, obtained zoning is the influence area at each control point；Control of the summit from the regional center in influence area
Point HiMaximum internal distance be control point HiSupport SZ (i)；To control point HiFor, other control points to HiIt is interior
The minimum value of portion's distance is HiIsolation distance GL (i)；
4.2) it is more than the control point of isolation distance, wherein control point H if there is supportjIt is (branch in above-mentioned control point
Degree of holding-isolation distance)/support value be maximum if, then in HjInfluence area in find out one from HjInner distance most
Big point, is generated in the above the empty control point of a first kind, the frame N (n at the empty control pointx,ny,nz) it is initialized as nx=(1,
0,0), ny=(1,0,0), nz=(1,0,0)；
4.3) iteration updates the support and isolation distance at each control point, then repeat step 4.2), until all controls
The support of system point is not more than its isolation distance；
4.4) for all control bones：The support difference at two real control points for simulating some control bone
For SZ1 and SZ2, d=min { SZ1, SZ2 } is taken, the length for controlling bone is L, ifAnd n ＞ 2, then in control bone
Equations of The Second Kind virtual controlling point, the frame N (n at such control point are inserted on the position of the n Along ents of bonex,ny,nz) initialization when the
One direction nxAlong the direction of the control bone, nx、nyAnd nzKeep vertical two-by-two；
4.5) step 4.3 is performed).
In step 5) in, the weight at the empty control point of real dominating pair of vertices is first calculated, dominating pair of vertices model vertices are then calculated again
Weight, comprise the following steps：
5.1) centered on control point, Voronoi diagram is obtained using Voronoi partitioning models region, the Voronoi is built
The dual graph DG of figure；
5.2) the mediation value for assigning real control point is 1, and the mediation value at empty control point is 0, by step 6.1) pair
The mediation value at real control point is distributed to empty control point by bigraph DG syntople using Laplace operator, then empty control
Point is normalized after obtaining the mediation value at each real control point, the obtained weight for the real dominating pair of vertices empty control point；
5.3) inner distances and definition of certain summit p to all control points on the resulting estimate model of model voxelization are passed through
For d1,d2,…,dm, m is the number at control point, control point HiTo p weight wiFor：
The function phi () of above formula is C2Continuous basic function, SZ (i) is the support at i-th of control point, and SZ (j) is the
The support at j control point, basic function φ () has following property：
φ (0)=1, and φ (t)=0,
φ'(t)≤0； (3)
φ " (t) is continuous in interval (0,1)；
φ ' (0)=φ ' (1)=φ " (0)=φ " (1)=0 (4)
Then basic function selection Bessel polynomial, the weight of each dominating pair of vertices model vertices is solved by equation (1).
In step 6) in, the real control point transformation of user's operation, empty control point response transform comprises the following steps：
6.1) user chooses real control point, can be become by translating the frame at real control point or the real control point of rotation
Change, obtain the transformation matrix T at r real control point1, T2..., Tr；
6.2) for i-th of first kind void control point HiRespond the conversion at real control point and convert, its transformation matrixTiFor empty control point HiTransformation matrix, qvFor empty control point HiRotation quaternary
Group, tvFor empty control point HiTranslation vector, wj(i) be j-th of real empty control point of i-th of first kind of dominating pair of vertices weight,
wsumIt is all real dominating pair of vertices virtual controlling point HiWeight sum；For the empty control point of Equations of The Second Kind, its center is located all the time
In on the Along ent of corresponding control bone, this is the strong constraint at the empty control point of Equations of The Second Kind, and its frame N (nx,ny,nz)
nxDirection also all the time along place control bone direction nx', take rotary shaft G=nx×nx', the anglec of rotationThe spin matrix R around rotary shaft G rotation alpha angles, the new frame N ' of Equations of The Second Kind spin matrix can then be tried to achieve
For N'=RN=R (nx,ny,nz)。
In step 7) in, it is necessary to reconstruction model, including try to achieve all m control points (including real control point and empty control point)
Transformation matrix T1, T2..., TmAfterwards, it is for the summit p of model new position p ' coordinate formulaThe w of above formulai(p) weight for being the i-th dominating pair of vertices summit p, TiFor the conversion square at i-th of control point
Battle array, p is the original coordinate position in summit, by above formula, using the parallel speed-up computations of GPU, completes model reconstruction.
The present invention compared with prior art, has the following advantages that and beneficial effect：
1st, the present invention goes 2 points in appraising model of inner distance using the method for model voxelization first.
2nd, present invention firstly provides use C2The method that continuous basic function display solves weight.
3rd, method of the present invention by generating empty control point, is reduced because the control point that user is arbitrarily set may be excessively close
Collection or excessively sparse possibility and cause model in editing process significantly to deform and not smooth excessive enough, empty control point
Generation enables to distribution of the weight on model more balanced and discrete.
4th, the present invention uses Voronoi partitioning models, and builds the dual graph of Voronoi diagram, passes through the neighbour of the dual graph
Connect relation and the mediation value at real control point is distributed to empty control point, so as to generate the weight at the empty control point of real dominating pair of vertices, reach
Real control point manipulates the effect at empty control point during to editor.
5th, the inventive method provides the transformation rule at empty control point first, it is specific special then under, the conversion at empty control point
It ensure that C2Editor's property of continuous weight, it is ensured that good edit effect so that edited result more conforms to user's
Demand, edit model when, the deformation of model is more reasonable.
6th, the inventive method, using the simple vertex update formula of algorithm is edited, uses GPU during reconstruction model
The new position of parallel speed-up computation model vertices, can dramatically improve computational efficiency, improve response during model editing
Speed, the feedback of model deformation can be provided the user with time, accomplishes the effect of real-time edition.
Brief description of the drawings
Fig. 1 is Shape Editing schematic flow sheet of the present invention.
Fig. 2 is the design sketch to being simulated after model hand bone discretization using real control point.
Fig. 3 a are to the schematic diagram (illustrating the model of input and the information of control bone) before model voxelization.
Fig. 3 b are to the schematic diagram after model voxelization.
The C that Fig. 4 selects for the present invention2The functional arrangement of continuous basic function.
Fig. 5 a are the model and control point schematic diagram of input.
Fig. 5 b are the state diagram behind the empty control point of generation.
Fig. 5 c divide figure for corresponding diagram 5a Voronoi area.
Fig. 5 d divide figure for corresponding diagram 5b Voronoi area.
Fig. 6 a are the control bone schematic diagram that user inputs.
Fig. 6 b render figure for the model to be edited of user's input.
Fig. 6 c are that user converts the state diagram that bone is controlled behind the real control point of control.
Fig. 6 d are the result figure of editor's algorithm reconstruction model.
Embodiment
With reference to specific embodiment, the invention will be further described.
As shown in figure 1, the weights C that the present embodiment is provided2Continuous linear hybrid shape editing method, including following step
Suddenly：
1) as shown in Figure 3 a, edit cell main Fig. 3 a is control bone, and the to be edited of user's input is read in first
Model, includes the face set of the vertex set, model of model；Described real control point and control bone refers to obtain user's input
The positional information at real control dot position information and control bone two ends.
2) discretization control bone, and simulation control bone is removed using real control point, as shown in Fig. 2 to model hand
Control after bone discretization, and simulation is gone using real control point, and initialize the frame at real control point, to for simulating control bone
The one of direction of frame at the real control point of bone must be along the weighting direction of the control bone of connection, two of such as Fig. 2
Shown in real control point frame, the frame at remaining real control point is directly simply set to (1,0,0), (0,1,0) and (0,0,1).
3) each summit of appraising model to real control point inner distance, as shown in Figure 3 b, to being caused after model voxelization
Close voxel result.2 points are all certain in two voxels of voxelization result inside model, utilize fine and close voxel knot
Really, 2 points in model of inner distance is estimated using the method for breadth first traversal.
4) the real control point of user's input is possible to excessively sparse or excessively dense, and constraint is unsatisfactory for for real control point
When, the empty control point of two classes of insertion comprises the following steps：
4.1) real control point and empty control point are referred to as control point, as shown in Figure 5 a the model for input and real control point,
Voronoi partitioning models region is used centered on control point, obtained zoning is the influence area at each control point；Shadow
Ring control point H of the summit from the regional center in regioniMaximum internal distance be control point HiSupport SZ (i)；It is right
Control point HiFor, other control points to HiInner distance minimum value be HiIsolation distance GL (i), as shown in Figure 5 c, be
The result divided to the Voronoi centered on Fig. 5 a real control point.
4.2) it is more than the control point of isolation distance, wherein control point H if there is supportjIt is (branch in above-mentioned control point
Degree of holding-isolation distance)/support value be maximum if, then in HjInfluence area in find out one from HjInner distance most
Big point, is generated in the above the empty control point of a first kind, the frame N (n at the empty control pointx,ny,nz) it is initialized as nx=(1,
0,0), ny=(1,0,0), nz=(1,0,0).
4.3) iteration updates the support and isolation distance at each control point, then repeat step 4.2), until all controls
The support of system point is not more than its isolation distance.
4.4) for all control bones：The support difference at two real control points for simulating some control bone
For SZ1 and SZ2, d=min { SZ1, SZ2 } is taken, the length for controlling bone is L, ifAnd n ＞ 2, then in control bone
Equations of The Second Kind virtual controlling point, the frame N (n at such control point are inserted on the position of the n Along ents of bonex,ny,nz) initialization when the
One direction nxAlong the direction of the control bone, nx、nyAnd nzKeep vertical two-by-two, such as Fig. 5 b so, to insert empty to Fig. 5 a
Result behind control point, and this figure is carried out after Voronoi divisions, obtain Fig. 5 d Voronoi area division figure.
5) weight at the empty control point of real dominating pair of vertices is first calculated, the weight of dominating pair of vertices model vertices is then calculated again, is wrapped
Include following steps：
5.1) centered on control point, Voronoi diagram is obtained using Voronoi partitioning models region, the Voronoi is built
The dual graph DG of figure.
5.2) the mediation value for assigning real control point is 1, and the mediation value at empty control point is 0, by step 6.1) pair
The mediation value at real control point is distributed to empty control point by bigraph DG syntople using Laplace operator, then empty control
Point is normalized after obtaining the mediation value at each real control point, the obtained weight for the real dominating pair of vertices empty control point.
5.3) inner distances and definition of certain summit p to all control points on the resulting estimate model of model voxelization are passed through
For d1,d2,…,dm, m is the number at control point, control point HiTo p weight wiFor：
The function phi () of above formula is C2Continuous basic function, SZ (i) is the support at i-th of control point, and SZ (j) is the
The support at j control point, basic function φ () has following property：
φ (0)=1, and φ (t)=0,
φ'(t)≤0； (3)
φ " (t) is continuous in interval (0,1)；
φ ' (0)=φ ' (1)=φ " (0)=φ " (1)=0 (4)
Then basic function selection Bessel polynomial, the weight of each dominating pair of vertices model vertices is solved by equation (1),
The basic function that this method is used is φ (t)=(1-t)5+5t(1-t)4+10t2(1-t)3, its functional image as shown in figure 4,
[0,1] functional value outside interval is 0, and the weight for trying to achieve dominating pair of vertices model vertices can be shown by basic function.
6) the real control point transformation of user's operation, empty control point response transform comprises the following steps：
6.1) user chooses real control point, can be become by translating the frame at real control point or the real control point of rotation
Change, obtain the transformation matrix T at r real control point1, T2..., Tr, it is as shown in Figure 6 a the original state of control bone, such as Fig. 6 b
The figure that renders for the model to be edited that user inputs is shown, user draws Fig. 6 c control bone by converting behind real control point
State.
6.2) for i-th of first kind void control point HiRespond the conversion at real control point and convert, its transformation matrixTiFor empty control point HiTransformation matrix, qvFor empty control point HiRotation quaternary
Group, tvFor empty control point HiTranslation vector, wj(i) be j-th of real empty control point of i-th of first kind of dominating pair of vertices weight,
wsumIt is all real dominating pair of vertices virtual controlling point HiWeight sum；For the empty control point of Equations of The Second Kind, its center is located all the time
In on the Along ent of corresponding control bone, this is the strong constraint at the empty control point of Equations of The Second Kind, and its frame N (nx,ny,nz)
nxDirection also all the time along place control bone direction nx', take rotary shaft G=nx×nx', the anglec of rotationThe spin matrix R around rotary shaft G rotation alpha angles, the new frame N ' of Equations of The Second Kind spin matrix can then be tried to achieve
For N'=RN=R (nx,ny,nz)。
7) reconstruction model, including try to achieve the transformation matrix T at all m control points (including real control point and empty control point)1,
T2..., TmAfterwards, it is for the summit p of model new position p ' coordinate formulaThe w of above formulai(p)
For the i-th dominating pair of vertices summit p weight, TiFor the transformation matrix at i-th of control point, p is the original coordinate position in summit, is passed through
Above formula, using the parallel speed-up computations of GPU, completes model reconstruction, Fig. 6 d are the result after model reconstruction.
In summary, the present invention provides new method for efficient mould shapes editor, it is allowed to which User Defined is set
Real control point and control bone, strict difinition model inner distance simultaneously use model voxelization method estimation inner distance.
During editor, the position at the real control point pre-set according to user and the empty control point of grey iterative generation, and provide empty control
The transformation rule of point.Empty control point enables to weight more balanced in the distribution of model area.C2Continuous weight causes editor
Result it is more smooth naturally, the original feature of model can accurately be kept, meet user's request, GPU parallel computations it is efficient
Editorial efficiency ensure user real-time edition.In a word, the present invention provides a kind of efficiently convenient in mould shapes editor field
Edit methods, feedback can be edited to user in time, the effect of real-time edition is reached, with actual application value, be worth pushing away
Extensively.
Embodiment described above is only the preferred embodiments of the invention, and the practical range of the present invention is not limited with this, therefore
The change that all shape, principles according to the present invention are made, all should cover within the scope of the present invention.
Claims (8)
1. a kind of weights C2Continuous linear hybrid shape editing method, it is characterised in that comprise the following steps：
1) Back ground Information is obtained, includes model, real control point and the control bone of user's input；
2) using real control point discretization control bone, and real control point is initialized；
3) inner distance of each summit of appraising model to real control point；
4) empty control point is generated；
5) weight and the weight of dominating pair of vertices model vertices at the empty control point of real dominating pair of vertices are calculated；
6) the real control point transformation of user's operation, empty control point response transform；
7) GPU accelerates reconstruction model parallel.
2. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 1) in, the model is the model to be edited of user's input, includes the face set of the vertex set of model, model；It is described
Real control point and control bone refer to the positional information for obtaining the real control dot position information of user's input and control bone two ends.
3. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 2) in, simulation control bone is removed with real control point, and real control point is initialized, comprises the following steps：
2.1) for the two ends of each control bone, simulation control bone is removed using two real control points respectively；
And then the real control point of initialization 2.2)：For for simulate control bone real control point, its frame N (nx,ny,nz)
First direction nxAlong the weighting direction of one or more control bones of connection, two other direction of frame is only needed
Meet with the orthogonal requirement two-by-two of first direction；For other real control points, frame N (nx,ny,nz)
Three directions are initialized as n respectivelyx=(1,0,0), ny=(0,1,0), nz=(0,0,1).
4. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 3) in, first to model voxelization, obtain the fine and close voxelization result of model, it is then excellent using range by the result of voxelization
The method first searched for goes to appraising model summit to the inner distance at each real control point.
5. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 4) in, user input real control point be possible to excessively sparse or excessively dense, for real control point be unsatisfactory for constraint
When, the empty control point of two classes of insertion comprises the following steps：
4.1) real control point and empty control point are referred to as control point, and Voronoi partitioning models region is used centered on control point,
Obtained zoning is the influence area at each control point；Control point H of the summit from the regional center in influence areai's
Maximum internal distance is control point HiSupport SZ (i)；To control point HiFor, other control points to HiInner distance
Minimum value be HiIsolation distance GL (i)；
4.2) it is more than the control point of isolation distance, wherein control point H if there is supportjIn being above-mentioned control point (support-
Isolation distance)/support value be maximum if, then in HjInfluence area in find out one from HjInner distance it is maximum
Point, is generated in the above the empty control point of a first kind, the frame N (n at the empty control pointx,ny,nz) it is initialized as nx=(1,0,
0), ny=(1,0,0), nz=(1,0,0)；
4.3) iteration updates the support and isolation distance at each control point, then repeat step 4.2), until all control points
Support be not more than its isolation distance；
4.4) for all control bones：Support for simulating the real control points of some control two of bone is respectively
SZ1 and SZ2, takes d=min { SZ1, SZ2 }, and the length for controlling bone is L, ifAnd n ＞ 2, then in control bone
N Along ents position on insert Equations of The Second Kind virtual controlling point, the frame N (n at such control pointx,ny,nz) initialization when first
Individual direction nxAlong the direction of the control bone, nx、nyAnd nzKeep vertical two-by-two；
4.5) step 4.3 is performed).
6. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 5) in, first calculate the weight at the empty control point of real dominating pair of vertices, then calculate the weight of dominating pair of vertices model vertices again, including with
Lower step：
5.1) centered on control point, Voronoi diagram is obtained using Voronoi partitioning models region, the Voronoi diagram is built
Dual graph DG；
5.2) the mediation value for assigning real control point is 1, and the mediation value at empty control point is 0, by step 5.1) dual graph DG
Syntople the mediation value at real control point is distributed to empty control point using Laplace operator, then empty control point acquisition
Normalized after the mediation value at each real control point, the obtained weight for the real dominating pair of vertices empty control point；
5.3) by certain summit p on the resulting estimate model of model voxelization to all control points inner distance and it is defined as d1,
d2,…,dm, m is the number at control point, control point HiTo p weight wiFor：
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</mrow>
</mrow>
The function phi () of above formula is C2Continuous basic function, SZ (i) is the support at i-th of control point, and SZ (j) is j-th of control
The support of point is made, basic function φ () has following property：
φ (0)=1, and φ (t)=0,
φ'(t)≤0； (3)
φ " (t) is continuous in interval (0,1)；
φ ' (0)=φ ' (1)=φ " (0)=φ " (1)=0 (4)
Then basic function selection Bessel polynomial, the weight of each dominating pair of vertices model vertices is solved by equation (1), is used
Basic function be φ (t)=(1-t)5+5t(1-t)4+10t2(1-t)3。
7. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 6) in, the real control point transformation of user's operation, empty control point response transform comprises the following steps：
6.1) user chooses real control point, is converted by translating the frame at real control point or the real control point of rotation, obtains r
The transformation matrix T at real control point1, T2..., Tr；
6.2) for i-th of first kind void control point HiRespond the conversion at real control point and convert, its transformation matrixTiFor empty control point HiTransformation matrix, qvFor empty control point HiRotation quaternary
Group, tvFor empty control point HiTranslation vector, wj(i) be j-th of real empty control point of i-th of first kind of dominating pair of vertices weight,
wsumIt is all real dominating pair of vertices virtual controlling point HiWeight sum；For the empty control point of Equations of The Second Kind, its center is located all the time
In on the Along ent of corresponding control bone, this is the strong constraint at the empty control point of Equations of The Second Kind, and its frame N (nx,ny,nz)
nxDirection also all the time along place control bone direction nx', take rotary shaft G=nx×nx', the anglec of rotationThe spin matrix R around rotary shaft G rotation alpha angles is then tried to achieve, the new frame N ' of Equations of The Second Kind spin matrix is
N'=RN=R (nx,ny,nz)。
8. a kind of weights C according to claim 12Continuous linear hybrid shape editing method, it is characterised in that：In step
It is rapid 7) in, it is necessary to reconstruction model, including try to achieve all m control points, include the transformation matrix T at real control point and empty control point1,
T2..., TmAfterwards, it is for the summit p of model new position p ' coordinate formulaW in formulai
(p) weight for being the i-th dominating pair of vertices summit p, TiFor the transformation matrix at i-th of control point, p is the original coordinate position in summit,
By above formula, using the parallel speed-up computations of GPU, model reconstruction is completed.
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